// Copyright 2014 The Chromium Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

#ifndef UI_GFX_GEOMETRY_CUBIC_BEZIER_H_
#define UI_GFX_GEOMETRY_CUBIC_BEZIER_H_

#include "base/macros.h"
#include "ui/gfx/gfx_export.h"

namespace gfx {

class GFX_EXPORT CubicBezier {
public:
    CubicBezier(double p1x, double p1y, double p2x, double p2y);
    CubicBezier(const CubicBezier& other);

    double SampleCurveX(double t) const
    {
        // `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
        return ((ax_ * t + bx_) * t + cx_) * t;
    }

    double SampleCurveY(double t) const
    {
        return ((ay_ * t + by_) * t + cy_) * t;
    }

    double SampleCurveDerivativeX(double t) const
    {
        return (3.0 * ax_ * t + 2.0 * bx_) * t + cx_;
    }

    double SampleCurveDerivativeY(double t) const
    {
        return (3.0 * ay_ * t + 2.0 * by_) * t + cy_;
    }

    // Given an x value, find a parametric value it came from.
    // x must be in [0, 1] range. Doesn't use gradients.
    double SolveCurveX(double x, double epsilon) const;

    // Evaluates y at the given x with default epsilon.
    double Solve(double x) const;
    // Evaluates y at the given x. The epsilon parameter provides a hint as to the
    // required accuracy and is not guaranteed. Uses gradients if x is
    // out of [0, 1] range.
    double SolveWithEpsilon(double x, double epsilon) const
    {
        if (x < 0.0)
            return 0.0 + start_gradient_ * x;
        if (x > 1.0)
            return 1.0 + end_gradient_ * (x - 1.0);
        return SampleCurveY(SolveCurveX(x, epsilon));
    }

    // Returns an approximation of dy/dx at the given x with default epsilon.
    double Slope(double x) const;
    // Returns an approximation of dy/dx at the given x.
    // Clamps x to range [0, 1].
    double SlopeWithEpsilon(double x, double epsilon) const;

    // Gets the bezier's minimum y value in the interval [0, 1].
    double range_min() const { return range_min_; }
    // Gets the bezier's maximum y value in the interval [0, 1].
    double range_max() const { return range_max_; }

    // These getters are used rarely. We reverse compute them from coefficients.
    // See CubicBezier::InitCoefficients. The speed has been traded for memory.
    double GetX1() const;
    double GetY1() const;
    double GetX2() const;
    double GetY2() const;

private:
    void InitCoefficients(double p1x, double p1y, double p2x, double p2y);
    void InitGradients(double p1x, double p1y, double p2x, double p2y);
    void InitRange(double p1y, double p2y);

    double ax_;
    double bx_;
    double cx_;

    double ay_;
    double by_;
    double cy_;

    double start_gradient_;
    double end_gradient_;

    double range_min_;
    double range_max_;

    DISALLOW_ASSIGN(CubicBezier);
};

} // namespace gfx

#endif // UI_GFX_GEOMETRY_CUBIC_BEZIER_H_
